8th Grade EOG Mathematics Test with Answer Key 2026-2027

 8th Grade Mathematics

End-of-Year Assessment

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Parent Preparation Guide & Complete Examination

 

 

Aligned To Texas TEKS Mathematics — Grade 8

Frameworks Used Bloom's Taxonomy Hess's Cognitive Rigor Matrix

 

FOR PARENTS: What Is This Document?   This guide contains a complete, rigorous 8th Grade mathematics examination aligned to the Texas Essential Knowledge and Skills (TEKS). It is designed to help parents understand what their child is expected to know by the end of 8th Grade and to prepare them for STAAR. Each question includes the specific TEKS standard, Bloom's Taxonomy level, Depth of Knowledge (DOK) level, a parent-friendly explanation of what the question measures, at-home support activities, and common mistakes to watch for.

 

 

 

PART 1: NUMBER & EXPONENTS

 

Student Name: ___________________________    Date: _______________    Grade: 8

 

Directions: Read each question carefully. Show all your work. For multiple-choice questions, circle the letter of the best answer. For open-response questions, write your answer and explanation in the space provided.

 

Question 1   Bloom's: Apply  |  DOK: 2  |  TEKS: 8.2A

Between which two consecutive integers does √47 lie? Without a calculator, explain your reasoning. Then determine whether √47 is rational or irrational.

A)  6 and 7 B)  7 and 8 C)  5 and 6 D)  8 and 9

 

Question 2   Bloom's: Apply  |  DOK: 2  |  TEKS: 8.2B

Write 0.000034 in scientific notation. Then write 2.15 × 10⁶ in standard form. Which number is larger?

Answer: _______________________________________________

 

Question 3   Bloom's: Analyze  |  DOK: 3  |  TEKS: 8.2D

Explain why 2⁻³ is NOT a negative number. What is its value? Now prove that (2³)(2⁻³) = 1 using the laws of exponents. What does this tell us about negative exponents?

Answer: _______________________________________________

 

 

PART 2: PROPORTIONALITY & LINEAR FUNCTIONS

 

Question 4   Bloom's: Apply  |  DOK: 2  |  TEKS: 8.4A

A line passes through the points (2, 5) and (6, 13).  A) Calculate the slope. B) Write the equation in slope-intercept form (y = mx + b). C) What is the y-intercept and what does it mean in context?

Answer: _______________________________________________

 

Question 5   Bloom's: Analyze  |  DOK: 3  |  TEKS: 8.4C

Two cell phone plans:    Plan A: y = 0.10x + 25 (x = minutes, y = monthly cost)    Plan B: y = 0.05x + 40  A) What does the slope mean in each plan? The y-intercept? B) For what number of minutes is Plan A cheaper? C) Graph both lines (describe the graph — where do they intersect?)

Answer: _______________________________________________

 

 

PART 3: EXPRESSIONS, EQUATIONS & SYSTEMS

 

Question 6   Bloom's: Apply  |  DOK: 2  |  TEKS: 8.9A

Solve the system of equations by substitution:    y = 3x - 4    2x + y = 11  Check your solution by substituting back into both original equations.

Answer: _______________________________________________

 

Question 7   Bloom's: Analyze  |  DOK: 3  |  TEKS: 8.9A

A system of equations can have one solution, no solution, or infinitely many solutions.  For each case below, determine the number of solutions WITHOUT solving. Explain how you know:    A) y = 2x + 5 and y = 2x - 3    B) y = 4x + 1 and 2y = 8x + 2    C) y = -x + 6 and y = 2x - 3

Answer: _______________________________________________

 

 

PART 4: GEOMETRY & MEASUREMENT

 

Question 8   Bloom's: Apply  |  DOK: 2  |  TEKS: 8.7A

A right triangle has legs of 9 cm and 12 cm. Use the Pythagorean Theorem to find the hypotenuse. Then verify: could the sides 5, 12, 13 form a right triangle? Show your work.

A)  15 cm; Yes B)  21 cm; Yes C)  15 cm; No D)  √153; Yes

 

Question 9   Bloom's: Analyze  |  DOK: 3  |  TEKS: 8.7C

A ladder 10 feet long leans against a wall. The base of the ladder is 6 feet from the wall.  A) How high up the wall does the ladder reach? B) If the base is moved to 8 feet from the wall (for safety), how high does it now reach? C) Which placement is safer? Which reaches higher? Is there a trade-off?

Answer: _______________________________________________

 

 

PART 5: DATA, STATISTICS & PROBABILITY

 

Question 10   Bloom's: Apply  |  DOK: 2  |  TEKS: 8.11A

The scatter plot data shows study time (x, in hours) and test scores (y):     (1,65), (2,70), (3,78), (4,80), (5,88), (6,92)  A) Describe the association (positive/negative, strong/weak, linear/nonlinear). B) Estimate the line of best fit equation. C) Predict the score for 7 hours of study.

Answer: _______________________________________________

 

Question 11   Bloom's: Evaluate  |  DOK: 3  |  TEKS: 8.11B

An advertisement claims: 'Students who use our tutoring service score 95% higher on tests!' The data shows: average score before = 60, average score after = 63.  A) Calculate the actual percent increase. B) Is the advertisement's claim accurate? What is misleading about it? C) Why might correlation in test score data not mean tutoring CAUSED the improvement?

Answer: _______________________________________________

 

 

PART 6: EXTENDED PROBLEM SOLVING

 

Question 12   Bloom's: Analyze  |  DOK: 3  |  TEKS: 8.4/8.7/8.9

A park design problem:  A rectangular park is 80 m × 60 m. A diagonal walking path crosses the park. A) How long is the diagonal path? B) A fence will cost $15/m along the perimeter and $22/m along the diagonal. What is the total fencing cost? C) The city can only spend $8,500 on fencing. Can they build the complete fence? By how much are they over or under budget?

Answer: _______________________________________________

 

Question 13   Bloom's: Create  |  DOK: 4  |  TEKS: All Domains

CAPSTONE PROJECT: Mathematical Modeling Challenge  You are a city planner. Design a plan for a small community park that includes:    (1) A rectangular main area with dimensions you choose    (2) A circular fountain in the center (you choose the radius)    (3) A diagonal walking path    (4) A budget analysis (you set realistic prices per unit)    (5) A linear equation modeling visitor count vs. days open    (6) A probability analysis: if 3 visitors are chosen randomly for a survey from a group of 5 men and 4 women, what is P(all 3 are women)?  All parts must be calculated, justified, and presented as a coherent plan.

Answer: _______________________________________________

 

 

COMPLETE ANSWER KEY

For Parent and Educator Use

 

 

Q#	Answer	Explanation	TEKS
1	A) 6 and 7; √47 is irrational.	6²=36, 7²=49. Since 36<47<49, then 6<√47<7. 47 is not a perfect square, so √47 is irrational (non-terminating, non-repeating decimal).	8.2A
2	0.000034 = 3.4 × 10⁻⁵. 2.15 × 10⁶ = 2,150,000. 2.15 × 10⁶ is vastly larger.	For 0.000034: move decimal 5 places right → 3.4 × 10⁻⁵. For 2.15×10⁶: move decimal 6 places right → 2,150,000.	8.2B
3	2⁻³ = 1/8 (positive). (2³)(2⁻³) = 2^(3+(-3)) = 2⁰ = 1. Negative exponents mean reciprocals: a⁻ⁿ = 1/aⁿ.	2⁻³ = 1/2³ = 1/8 ≈ 0.125. Not negative — it's a positive fraction. Product rule: 2³ × 2⁻³ = 2⁰ = 1, confirming that 2³ and 2⁻³ are reciprocals.	8.2D
4	A) m = 2. B) y = 2x + 1. C) y-intercept = 1 — when x=0, y=1 (the starting value).	m = (13-5)/(6-2) = 8/4 = 2. Using (2,5): 5 = 2(2)+b → b=1. Equation: y=2x+1.	8.4A
5	A) Slope=cost per minute; y-intercept=base fee. B) Plan A cheaper when x<300. C) Lines intersect at (300, 55).	Set equal: 0.10x+25=0.05x+40 → 0.05x=15 → x=300. At 300 min both cost $55. Below 300, A is cheaper. Above, B is cheaper.	8.4C
6	x = 3, y = 5. Check: y=3(3)-4=5 ✓. 2(3)+5=11 ✓.	Substitute: 2x + (3x-4) = 11 → 5x-4=11 → 5x=15 → x=3. y=3(3)-4=5. Solution: (3,5).	8.9A
7	A) No solution (parallel lines — same slope, different intercepts). B) Infinite solutions (same line). C) One solution (different slopes → intersect).	A) Both slope=2, different intercepts → parallel. B) Divide second by 2: y=4x+1 — identical to first → same line. C) Slopes -1 and 2 differ → one intersection point.	8.9A
8	A) 15 cm; Yes (5²+12²=25+144=169=13²).	9²+12²=81+144=225=15². Hyp=15. Check: 5²+12²=169=13². Yes, right triangle.	8.7A
9	A) √(100-36)=√64=8 ft. B) √(100-64)=√36=6 ft. C) Farther base = safer but lower reach. Trade-off between safety and height.	Pythagorean: 6²+h²=10² → h=8. 8²+h²=10² → h=6. As base increases, height decreases. This illustrates the inverse relationship — a real trade-off in ladder safety.	8.7C
10	A) Strong positive linear association. B) Approx: y = 5.5x + 59. C) ≈ 97.5.	The data increases steadily and nearly linearly. Slope ≈ (92-65)/(6-1) = 27/5 = 5.4. Using (1,65): 65=5.4(1)+b → b≈59.6. Predict 7 hrs: 5.5(7)+59=97.5.	8.11A
11	A) (63-60)/60 = 5% increase. B) Claim is false (95% vs. 5%). C) Other factors (harder study habits, better sleep, teacher change) may have caused improvement — correlation ≠ causation.	Actual increase: 5%. The ad falsely claimed 95%. Also: students who seek tutoring may also study harder independently. Self-selection bias means the improvement may not be caused by the tutoring itself.	8.11B
12	A) 100 m. B) Perimeter: $4,200. Diagonal: $2,200. Total: $6,400. C) Under budget by $2,100.	A) √(80²+60²)=√(6400+3600)=√10000=100m. B) Perimeter: 2(80+60)=280m × $15=$4,200. Diagonal: 100×$22=$2,200. Total=$6,400. Under $8,500 by $2,100.	8.4/8.7/8.9
13	Answers vary. Full credit: valid geometry calculations, complete budget, linear equation with interpretation, P(all 3 women) = (4/9)(3/8)(2/7) = 24/504 = 1/21 ≈ 4.76%.	P(1st woman)=4/9. P(2nd|1st)=3/8. P(3rd|first two)=2/7. Combined: 4/9×3/8×2/7=24/504=1/21. All geometry and budget should be internally consistent with student's chosen dimensions.	All Domains

 

 

PARENT GUIDE

Understanding Every Question: What It Measures & How to Help

 

 

Q1: Estimating Irrational Square Roots TEKS 8.2A  |  Bloom's: Apply | DOK: 2

What This Question Measures: Students reason about irrational numbers without a calculator — understanding that most square roots are irrational and developing number sense about their approximate location on the number line. How to Help Your Child at Home: Practice perfect squares (1,4,9,16,25,36,49,64,81,100). Then estimate: 'Between which two perfect squares does 50 fall? 75? 30?' The pattern of reasoning (comparison to perfect squares) is the key skill. Watch For / Common Mistakes: Students may compute a decimal approximation on a calculator without engaging the conceptual reasoning. Require them to FIRST explain using perfect squares, THEN verify with a calculator.

 

Q2: Scientific Notation — Very Small and Very Large Numbers TEKS 8.2B  |  Bloom's: Apply | DOK: 2

What This Question Measures: Scientific notation is the language of science — used for atomic measurements, astronomical distances, and everything in between. Students must convert in both directions and compare magnitudes. How to Help Your Child at Home: Look up real measurements: diameter of a human hair (~0.00007 m = 7×10⁻⁵ m), distance to the sun (~150,000,000 km = 1.5×10⁸ km). Convert back and forth. Connect to science class! Watch For / Common Mistakes: For small numbers, students often write the exponent as positive (3.4 × 10⁵ instead of 10⁻⁵). The decimal moved RIGHT (toward larger) → NEGATIVE exponent. Think: making a tiny number requires a negative power of 10.

 

Q3: Negative Exponents — Understanding the Pattern TEKS 8.2D  |  Bloom's: Analyze | DOK: 3

What This Question Measures: DOK 3 — students must explain, prove, and derive the meaning of negative exponents from the laws of exponents. This is conceptual understanding of exponents at its deepest level. How to Help Your Child at Home: Build a table: 2⁴=16, 2³=8, 2²=4, 2¹=2, 2⁰=1, 2⁻¹=?, 2⁻²=? Ask: 'Each step we divide by 2. What comes after 1? After 1/2?' Let the pattern reveal the meaning of negative exponents. Watch For / Common Mistakes: 'Negative exponent means negative number' is the most persistent misconception. 2⁻³ = 1/8 = 0.125 — positive, less than 1. Use the table approach to let students discover the pattern rather than just memorizing the rule.

 

Q4: Slope-Intercept Form — Writing Linear Equations TEKS 8.4A  |  Bloom's: Apply | DOK: 2

What This Question Measures: Students find slope, write linear equations, and interpret the y-intercept — core 8th grade algebra skills that connect to every STEM field and to the modeling of real-world change over time. How to Help Your Child at Home: Graph real data: your child's height at different ages, temperature throughout the day, distance over time on a walk. Find the slope (rate of change) and y-intercept (starting value). Make linear equations come alive. Watch For / Common Mistakes: Students often subtract coordinates in the wrong order for slope: (y₁-y₂)/(x₁-x₂) instead of (y₂-y₁)/(x₂-x₁). Both are correct IF consistent — but mixing orders is the error. Teach a consistent procedure.

 

Q5: Interpreting Linear Equations — Slope and Intercept in Context TEKS 8.4C  |  Bloom's: Analyze | DOK: 3

What This Question Measures: Students interpret slope and y-intercept in a real-world context AND find the intersection of two linear equations — combining graphical, algebraic, and contextual understanding. How to Help Your Child at Home: Compare two actual phone or subscription plans your family uses. Identify fixed cost and per-unit cost. Write equations. Find when they're equal. Decide which plan suits your usage. This is exactly how adults make contract decisions. Watch For / Common Mistakes: Students may solve the system algebraically but then fail to interpret the meaning: 'Plan A is cheaper for fewer than 300 minutes.' The mathematical answer (x=300) must be connected to the real-world decision.

 

Q6: Systems of Equations — Substitution Method TEKS 8.9A  |  Bloom's: Apply | DOK: 2

What This Question Measures: Students solve a 2×2 system of linear equations using substitution — a foundational algebra skill directly tested on STAAR and required for all high school mathematics. How to Help Your Child at Home: Present as a puzzle: 'Two numbers. The first is 3 times the second minus 4. Together, double the second plus the first equals 11. Find both numbers.' Algebra as puzzle-solving makes it engaging. Watch For / Common Mistakes: The most common error: after finding x=3, students substitute into one equation and stop without verifying the second. Checking both equations is not optional — it builds mathematical rigor and catches errors.

 

Q7: Classifying Systems of Equations — Geometric Reasoning TEKS 8.9A  |  Bloom's: Analyze | DOK: 3

What This Question Measures: DOK 3 — students analyze the structure of linear equations to predict the number of solutions without solving — a sophisticated geometric insight connecting algebra to the visual behavior of lines. How to Help Your Child at Home: Graph all three systems together. Let your child see that parallel lines never meet, identical lines overlap everywhere, and lines with different slopes always cross. The visual makes the algebraic reasoning intuitive. Watch For / Common Mistakes: Students may try to solve each system algebraically — which works but misses the conceptual point. Push them to compare slopes and intercepts FIRST. This is faster AND demonstrates deeper understanding.

 

Q8: Pythagorean Theorem — Application and Verification TEKS 8.7A  |  Bloom's: Apply | DOK: 2

What This Question Measures: Students apply the Pythagorean Theorem to find a missing side AND verify whether three given lengths form a right triangle — two distinct but related skills essential for geometry and trigonometry. How to Help Your Child at Home: Measure diagonals of rectangular objects. Verify: if a TV is 16 inches wide and 12 inches tall, the diagonal should be 20 inches. Check it! This makes the theorem physically real and memorable. Watch For / Common Mistakes: Students often use the formula as a + b = c (adding, not squaring). The squares are essential: a² + b² = c². Also: the hypotenuse is ALWAYS the longest side — if students get a hypotenuse shorter than a leg, they've made an error.

 

Q9: Pythagorean Theorem — Design Trade-offs in Real Engineering TEKS 8.7C  |  Bloom's: Analyze | DOK: 3

What This Question Measures: Students apply the theorem twice and analyze a real trade-off — higher safety means lower reach. This is engineering reasoning using geometry: understanding that design decisions involve competing constraints. How to Help Your Child at Home: Look up ladder safety guidelines (OSHA recommends a 4:1 ratio — for every 4 feet of height, base should be 1 foot out). Calculate: at 8 feet high, the safe base is 2 feet. Does this match our calculation? Watch For / Common Mistakes: Students may correctly find heights but then struggle to articulate the trade-off. Require a clear sentence: 'Moving the base farther makes the ladder safer but it reaches less high.' The qualitative conclusion matters as much as the numbers.

 

Q10: Scatter Plots, Association, and Lines of Best Fit TEKS 8.11A  |  Bloom's: Apply | DOK: 2

What This Question Measures: Students analyze scatter plot patterns, describe the association, estimate a line of best fit, and make predictions — core data literacy skills that bridge statistics, algebra, and real-world reasoning. How to Help Your Child at Home: Collect your own data over several weeks (study time vs. quiz scores, sleep vs. performance). Plot it. Draw a line of best fit. Make predictions. Compare predictions to actual results. This is real scientific method. Watch For / Common Mistakes: Students may draw a line connecting only the first and last points, ignoring the middle data. The line of best fit should be drawn through the MIDDLE of the data, with roughly equal numbers of points above and below.

 

Q11: Statistical Reasoning — Evaluating Claims, Causation vs. Correlation TEKS 8.11B  |  Bloom's: Evaluate | DOK: 3

What This Question Measures: DOK 3 — students evaluate a real-world advertising claim using statistics, compute an accurate percent, identify misleading language, and distinguish correlation from causation — the most sophisticated statistical thinking in 8th grade. How to Help Your Child at Home: Collect real misleading statistics from advertisements or news. Compute what the numbers actually say. Discuss: 'Could something else explain this? Could the data be true but presented misleadingly?' This is critical media literacy. Watch For / Common Mistakes: Students may accept '95% higher' without computing the actual change. The habit of VERIFYING statistical claims — not accepting them at face value — is the most important life skill this course teaches.

 

Q12: Pythagorean Theorem + Perimeter + Budget — Engineering Design TEKS 8.4/8.7/8.9  |  Bloom's: Analyze | DOK: 3

What This Question Measures: Students integrate the Pythagorean Theorem, perimeter, and financial reasoning in a multi-part engineering design problem — the kind of integrated, realistic problem that defines real-world mathematical modeling. How to Help Your Child at Home: Design your ideal park or room on graph paper. Add a diagonal path or feature. Calculate all dimensions using the Pythagorean Theorem. Research realistic costs for materials. Determine if your design fits your budget. Watch For / Common Mistakes: Students may forget to include BOTH the perimeter fence AND the diagonal fence, or may compute the diagonal as 80+60=140 instead of √(80²+60²)=100. Emphasize: the diagonal of a rectangle is NOT the sum of the two sides.

 

Q13: City Park Design — Full Mathematical Modeling Capstone TEKS All Domains  |  Bloom's: Create | DOK: 4

What This Question Measures: Bloom's CREATE at DOK 4 — the ultimate 8th grade mathematical challenge. Students design a real-world system using geometry, algebra, probability, and financial reasoning. This is authentic mathematical modeling: the work real engineers, architects, and city planners do. How to Help Your Child at Home: This can be a family project! Design your dream community park together. Research real costs for fencing, fountains, and paving. Calculate everything. Present it as a real proposal — to a 'city council' of family members. Make mathematics a creative, collaborative act. Watch For / Common Mistakes: Internal consistency is key: if the student chooses a 100m × 80m park, all subsequent calculations must use those dimensions. A beautiful plan with correct math earns full credit. Make sure the probability in Part 6 uses the without-replacement method (conditional probability).

 

 

Scoring Guide & Next Steps

 

 

Score	Performance Level	Recommended Action
27–30	Masters Grade Level	Excellent! Focus on enrichment and extension. Explore real-world applications and the next grade's preview topics.
22–26	Meets Grade Level	Strong! Review missed questions by domain. Use the Parent Guide tips for weak areas.
16–21	Approaches Grade Level	Spend 15 minutes daily on the domains where most questions were missed. Use hands-on activities from the guide.
0–15	Developing Foundational Skills	Schedule time with the teacher. Focus on the first two TEKS domains — they are the foundation for everything else.

 

 

 

This guide was developed using Texas TEKS Mathematics standards for Grade 8, Bloom's Revised Taxonomy, and Hess's Cognitive Rigor Matrix. All questions are original and written to mirror STAAR-aligned rigor. Designed to bridge classroom learning and home support.